“Trigonometry Values Pi/11”的概念、定义、习题解题方法及翻译-数学辞典

单词

Trigonometry Values Pi/11

释义

Trigonometry Values Pi/11

Trigonometric functions of for an integer cannot be expressed in terms of sums, products, and finite rootextractions on real rational numbers because 11 is not a Fermat Prime. This also means that the Undecagon is nota Constructible Polygon.

However, exact expressions involving roots of complex numbers can still be derived using the trigonometric identity


	(1)

Using the identities from Beyer (1987, p. 139),

(2)

(3)

gives




	(4)

Now, let

and

, then

(5)

This equation is an irreducible Quintic Equation, so an analytic solution involving Finite Rootextractions does not exist. The numerical Roots are

, 0.29229, 0.57115, 0.82743, 0.97974. So

. Fromone of Newton's Identities,

	(6)
	(7)
	(8)

The trigonometric functions of

also obey the identity

(9)

See also Undecagon

References

Beyer, W. H. ``Trigonometry.'' CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, 1987.

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